The slogan that hung from bridges and balconies all over Madrid read “Never stop believing” and Atlético never did, even when they might have feared it would be taken from them in the final minute. Few know how to suffer like they do but few know how to make opponents suffer like they do either. The pressure built and the Calderón kept singing, Diego Simeone sometimes as much a conductor as a coach amid the tension of the final minutes, but they have done it again.

Two goals from Antoine Griezmann, one in each half, took them into the Champions League semi-finals. And they will believe that their journey need not end there, the coach calling this “a step, but no more than that”. Their rebellion against the game’s aristocracy continues and it is one that Simeone insists is about more than just football; this team, cup winners, league champions and European Cup semi-finalists in under four years, offers a lesson in life.

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“I would look beyond the fact that we have reached a semi-final to values which are ever rarer in society,” Simeone said. “We can win or lose but we believe in the values life teaches you: respect, perseverance, the willingness to get up again, the ability to persist even against those more talented, to compete. I said to the players: you have great values as individuals and as a group. We never stopped believing.”

As for Barcelona, their belief in a second treble was extinguished here. For only the second time in eight years they have failed to reach the semi-finals; both times they were eliminated at this stage by Atlético. There will be much to pick over after the referee, Nicola Rizzoli, judged that a handball from Gabi in the 91st minute had occurred outside the area, not in it. Messi took the free-kick he was given, not the penalty he wanted, and sent Barcelona’s last chance over the bar. Four nervous minutes later this stadium erupted once more. There could be few complaints, though. Atlético celebrated, Barcelona watched their hopes of a second Champions League in a row disappear. “I am 99.9% to blame . . . no, 100%,” Luis Enrique said. He insisted that “two very nice objectives” remain but, while they are well placed, there will be doubts about them winning the league and the Copa del Rey now. They have not won in three league games and they appear riddled with uncertainty. Here, too, it was tense and there were nerves until the very end but ultimately Atlético deserved their victory, seeking it from the start. Barcelona did not. Simeone’s side had three attempts on goal inside seven minutes. The home side had chosen to attack; the visitors’ plan appeared to be to anaesthetise. It did not work. Barcelona had an immense majority of the ball but they moved it slowly and from deep and Atlético’s opener rendered the tactic redundant. Saúl’s beautiful pass, with the outside of his boot, was headed into the net by Griezmann after 36 minutes.

Barcelona did not even have an attempt on target until Neymar’s swinging effort on 41 minutes and there was still time for Atlético to frighten them once more when Yannick Carrasco burst from deep and Saúl hit the bar after the break. The second half was different – “more the way they wanted it than the way we did,” as Simeone put it – but breaking down Atlético is a huge task and Barcelona were unable to manage it.

Luis Suárez and Jordi Alba combined for the full-back to send the ball across the six-yard box where Gabi cleared. Diego Godín then blocked Alba’s shot and Jan Oblak saved twice from Andrés Iniesta. The pace and pressure built, yet few chances were clear-cut and the threat on the counter had already been made clear when Griezmann raced away to be stopped by Marc-André Ter Stegen before Filipe Luis did likewise in the 88th minute, forcing a penalty when Iniesta handballed.

Griezmann scored but it was not over yet. Three minutes later Barcelona appealed for a penalty that would have sent this to extra time. Iniesta’s shot hit Gabi’s arm. It appeared to be inside the area but a free-kick was given outside. Messi struck over, Atlético went through.